How do you find #f(g(-3))# given #f(x)=2x-1# and #g(x)=3x# and #h(x)=x^2+1#?

Answer 1

Evaluate f(g(-3)) by substituting -3 into g(x), then take that result and substitute it into f(x). The final expression is 15.

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Answer 2

Isaiah Anthony

See a solution process below:

First, find #g(-3)# by substituting #color(red)(-3)# for each occurrence of #color(red)(x)# in #g(x)#:

#g(color(red)(x)) = 3color(red)(x)# becomes:

#g(color(red)(-3)) = 3 xx color(red)(-3)#

#g(color(red)(-3)) = -9#

Therefore: #f(g(-3)) = f(-9)#

Because #g(-3) = -9# then f(g(-3)) = f(-9)#

To find #f(-9)# we can substitute #color(red)(-9)# for each occurrence of #color(red)(x)# in #f(x)#

#f(color(red)(x)) = 2color(red)(x) - 1# becomes:

#f(color(red)(-9)) = (2 xx color(red)(-9)) - 1#

#f(color(red)(-9)) = -18 - 1#

#f(color(red)(-9)) = -19#

#f(g(-3)) = -19#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.