Question

Let f(x) = 5x + 12. Find f−1(x).

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

Let f(x) = twenty four over the quantity of 3 x minus two. Find f(−2).

Can Someone explain how to do this? Thanks

Answer 1

Hello,

1)
y=5x+12
Exchanging x to y and y to x, we have x=5y+12
And now solve for y: y=(x-12)/5

f^(-1)(x)=(x-12)/5

2)
f(x)=x+8
g(x)=x²-6x-7

fog(x)=f(g(x))=f(x²-6x-7)= (x²-6x-7)+8=x²-6x+1

f(g(2))= 2²-6*2+1=4-12+1=-7

3)
f(x)=24/(3x-2)

f(-2)=24/(3*(-2)-2)=24/(-8)=-3