Question

It's not a really a question but how to solve these types of questions

Let f(x) = 9x − 2 and g(x) = −x + 3. Find f(g(x)).

Let f(x) = 2x + 2. Solve f−1(x) when x = 4.

Let f(x) = x + 8 and g(x) = x2 − 6x − 7. Find f(g(2)).

Let f(x) = x2 − 8x + 5. Find f(−1).

Answer 1

1. 9(-x+3) - 2
3.[ (2)2 - 6(2) - 7] + 8
4.(-1)2 - 8(-1) + 5

Answer 2

Part 1)
`f(x) = 9x- 2` and
`g(x) = -x + 3`

Find f(g(x)).

`f(x) = 9x- 2`

Substitute value of g(x) in place of x

`f(g(x)) = 9(-x+3)- 2`

`f(g(x)) = -9x+27- 2`

`f(g(x)) = -9x+25`

So,
`f(g(x)) = -9x+25`

Part 2)
`f(x) = 2x + 2`

`y = 2x + 2`

Replace y with x and x with y

`x = 2y + 2`

Find y

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

So,
`f^(-1)(x)=(x-2)/(2)`

Substitute x = 4

`f^(-1)(4)=(4-2)/(2)`

`f^(-1)(4)=1`

Part 3)
`f(x) = x + 8` and
`g(x) = x^2- 6x-7`

`f(x) = x + 8`

Substitute value of g(x) in place of x

`f(g(x)) =x^2- 6x-7 + 8`

`f(g(x)) =x^2- 6x+1`

Substitute x = 2

`f(g(x)) =2^2- 6(2)+1`

`f(g(x)) =4- 12+1`

`f(g(x)) =-7`

Part 4)
`f(x) = x^2-8x + 5`

Substitute x = -1

`f(-1) = (-1)^2-8(-1) + 5`

`f(-1) =14`