Given f(x)=4x-3, g(x)=1/x and h(x)= x^2-x, how do you find f [h(4)]?

Oct 9, 2017

$f \left[h \left(4\right)\right] = 45$

Explanation:

First, you need to find $h \left(4\right)$, by subbing in $4$ every time you see $x$.

$h \left(x\right) = {x}^{2} - x$

$h \left(4\right) = {4}^{2} - 4$

$h \left(4\right) = 16 - 4$

$\therefore h \left(4\right) = 12$

Now that we have $h \left(4\right)$, we can figure out $f \left[h \left(4\right)\right]$.

$f \left(x\right) = 4 x - 3$

$f \left[h \left(4\right)\right] = 4 x - 3$

$f \left(12\right) = 4 \left(12\right) - 3$

$f \left(12\right) = 48 - 3$

$\therefore f \left[h \left(4\right)\right] = 45$