Question

Let h(x) = 2x + 5 and g(x) = 8 - 3r. What is the value of h(g(1.5))?​

Answer 1

Answer: 12

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Explanation:

First lets compute the value of g(1.5)

Plug x = 1.5 into the g(x) function

g(x) = 8 - 3x

g(1.5) = 8 - 3*1.5  <<--- note how every x is replaced with 1.5

g(1.5) = 8 - 4.5

g(1.5) = 3.5

We ultimately want the value of h(g(1.5)), but that is the same as h(3.5) because we found g(1.5) = 3.5; effectively, g(1.5) and 3.5 are the same value.

Let's compute h(3.5) by plugging in x = 3.5 into the h(x) function.

h(x) = 2x + 5

h(3.5) = 2(3.5) + 5

h(3.5) = 7+5

h(3.5) = 12

h(g(1.5)) = 12 which is the final answer

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An alternative track is to first figure out what h(g(x)) would be in general, by first doing this

h(x) = 2x + 5

h(g(x)) = 2*( g(x) ) + 5  <<---- every x replaced with g(x)

h(g(x)) = 2*( 8-3x ) + 5 <<---- the g(x) replaced with 8-3x

h(g(x)) = 16 - 6x + 5

h(g(x)) = -6x + 21

From here, we plug in x = 1.5

h(g(x)) = -6x + 21

h(g(1.5)) = -6*1.5 + 21

h(g(1.5)) = -9 + 21

h(g(1.5)) = 12 which is the same answer as before