# If h(x)=3^(2x) and f(x)=x-2, how do you find h(f(-3))?

Mar 30, 2018

$h \left(f \left(- 3\right)\right) \cong 0.000017$

#### Explanation:

When we evaluate a function, we substitute in a value.

$h \left(f \left(x\right)\right)$ means 'evaluate $f \left(x\right)$ first, then evaluate $h \left(\text{that answer}\right)$'.

So first, we know $x = - 3$

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

We substitute in $- 3$ where we see $x$, so $f \left(- 3\right) = \left(- 3\right) - 2 = - 5$

Now we evaluate $h \left(f \left(x\right)\right) = h \left(- 5\right)$.

$h \left(x\right) = {3}^{2 x}$ and we substitute in $- 5$ wherever we see $x$:

$h \left(x\right) = {3}^{2} \left(- 5\right) = {3}^{-} 10 = \frac{1}{3} ^ 10 \cong 0.000017$