Question

If h(x)=3x+2 and h(f(x))=x then f(2)=?

if h(x)=3x+2 and h(f(x))=x then f(2)=?

Answer 1

`f(2) = 0`

Explanation:

`h(f(x) ) = x`

`=> f(x) = h^(-1) (x)` The inverse function

Find the inverse function of `h(x)`

`x = 3y +2`

`y = (x-2)/3`

`h^(-1) (x) = 1/3 ( x-2)`

`f(2) = h^(-1)(2) = 1/3(2-2) = 0`

Answer 2

`f(2)=0`

Explanation:

`"since "h(x)=3x+2" let "f(x)=ax+b`

`"then "h(f(x)=3(ax+b)+2=3ax+3b+2`

`"but "h(f(x))=x`

`color(blue)"comparing coefficients ""gives"`

`3a=1rArra=1/3`

`3b+2=0rArrb=-2/3`

`"thus "f(x)=1/3x-2/3rArrf(2)=2/3-2/3=0`