Question

What is f–1(8)??

Please select the best answer

Answer 1

Choice B is correct answer.

Explanation:

From question statement , we observe that

A function is given and we have to find inverse of this function. Then, we have to find the f⁻¹(8).

f(x) = 2x+5

put f(x) = y in above equation, we get

y = 2x+5

adding -5 to both sides of above equation,we get

y-5 = 2x+5-5

y-5 = 2x

dividing by 2 to both sides of equation,we get

y-5 / 2 = 2x/ 2

y-5 / 2 = x

swapping equation,we get

x = y-5 / 2

put f⁻¹(y) = x in above equation,we get

f⁻¹(y) = y-5 / 2

replace y with x in above equation

f⁻¹(x) = x-5 / 2

we have to find f⁻¹(8) .

putting x = 8 in above equation,we get

f⁻¹(8) = 8-5/2

f⁻¹(8) = 3/2 which is the answer.

Answer 2

`f^(-1)(8)=(3)/(2)`

Explanation:

Given f(x)=
`2x+5`

We have to find
`f^(-1)(8)`

In order to find
`f^(-1)(x)` we have to make x as the subject of the formula

Let us assume f(x)=y

⇒
`2x+5=y`

Subtracting both sides by 5

`2x+5-5=y-5`

`2x=y-5`

Dividing both sides by 2

`(2x)/(2)=(y-5)/(2)`

⇒
`x=(y-5)/(2)`

Now substituting y with x

we have
`f^(-1)(x)=(x-5)/(2)`

Now
`f^(-1)(8)=(8-5)/(2)`

=
`(3)/(2)`

So option (ii) is correct