Question
The functions f and g are defined by f(x) = 4x and g(x)= x2. For what value of x does f (x)– g( x) =4 ?
- -2
- -1
- 1
- 2
Hint:
Hint:
We need to find the value of which satisfies 
. We are given expressions of 
and 
. We simply need to input
these values in the given equation and solve it for x . As this value of x satisfies both and , this value of x will obviously satisfy
The correct answer is: 2
Step by step solution:
The given functions are 
and 
These functions are satisfied by all values of x .
So, a particular value of x satisfies .
Hence, the value of the function will satisfy
That is,
Writing the above equation in standard form,
We solve the above equation by using middle term factorisation.
Taking common from the first two terms and common from the last two terms, we have
The equation becomes
The solution of the above equation is given by
This gives
The correct option is D)
Note:
Instead of solving the equation in the above way, we could also use the quadratic formula, given by
Where the quadratic equation is given by
Or we could simply observe that it the expression of a perfect square
Related Questions to study
Find the co-ordinates of the mid-point of AB, if A ≡ (1, 10) and B ≡ (3, -8).
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The adjacent sides of a parallelogram are 8cm and 9cm. The diagonal joining the ends of these sides is 13cm. Calculate the area of the parallelogram.
The adjacent sides of a parallelogram are 8cm and 9cm. The diagonal joining the ends of these sides is 13cm. Calculate the area of the parallelogram.
Note:
Instead of adding 2 on both sides, we can also understand the concept by taking -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x from the left hand side to the right hand side, and here it becomes - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
Note:
Instead of adding 2 on both sides, we can also understand the concept by taking -2 of the right hand side on the left hand side and then the sign changes to + 2 . Similarly, instead of subtracting both sides by , we can understand it by saying that we take + x from the left hand side to the right hand side, and here it becomes - x .
Thus, addition becomes subtraction and vice-versa when taken from left hand side to right hand side or the opposite way; and multiplication becomes division and vice-versa. Be careful, 0 is never taken in the denominator.
Find the value of x that satisfies the equation 7x + 22 = − 27 .
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The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10cm . If its altitude is 8cm, what is its area?
The perimeter of a trapezium is 52 cm and its non-parallel sides are each equal to 10cm . If its altitude is 8cm, what is its area?
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Joe’s age is 16 years less than 5 times Jim’s age. Find Jim’s age if Joe is 9 years old.
Are the two polygons congruent? Explain why or why not.
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Which of the following expressions is equivalent to the expression above?
Note:
Another way of solving this problem is to expand all the terms in the expression
Then we get,
Thus, we will get that
Can be written as
This also gives the same answer as above. No matter which method we use to simplify the expression, we will always get a unique answer.
Which of the following expressions is equivalent to the expression above?
Note:
Another way of solving this problem is to expand all the terms in the expression
Then we get,
Thus, we will get that
Can be written as
This also gives the same answer as above. No matter which method we use to simplify the expression, we will always get a unique answer.
△ DEF ≅ △ LMN
m∠D = m∠L = 70°
m∠F = m∠N = 30°
Which of the following statements is NOT true?
△ DEF ≅ △ LMN
m∠D = m∠L = 70°
m∠F = m∠N = 30°
Which of the following statements is NOT true?
The parallel sides of a trapezium are 30cm and 10cm and the other two sides are 13cm, 21cm .find its area?
The parallel sides of a trapezium are 30cm and 10cm and the other two sides are 13cm, 21cm .find its area?
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One hundred park-district members will be selected to participate in a survey about selecting a new park-district coordinator. Which of the following methods of choosing the 100 members would result in a random sample of members of the park district?
Note:
The method given is option A is called simple random sampling. Some other methods of random sampling are stratified random sampling, cluster random sampling and systematic random sampling.
Infact, there is further categorisation of simple random sampling- probability and non-probability sampling.
One hundred park-district members will be selected to participate in a survey about selecting a new park-district coordinator. Which of the following methods of choosing the 100 members would result in a random sample of members of the park district?
Note:
The method given is option A is called simple random sampling. Some other methods of random sampling are stratified random sampling, cluster random sampling and systematic random sampling.
Infact, there is further categorisation of simple random sampling- probability and non-probability sampling.
