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

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Answer 1 · 2018-03-30T05:16:58

#h(f(-3))~=0.000017#

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

#h(f(x))# means 'evaluate #f(x)# first, then evaluate #h("that answer")#'.

So first, we know #x=-3#

Then #f(x)=f(-3)#

We substitute in #-3# where we see #x#, so #f(-3)=(-3)-2=-5#

Now we evaluate #h(f(x))=h(-5)#.

#h(x)=3^(2x)# and we substitute in #-5# wherever we see #x#:

#h(x)=3^2(-5)=3^-10 =1/3^10~=0.000017#