Question

Let t(x) = 3x-8 and s(t(x)) = x^2 + 3x - 2. Find s(1).

Answer 1

Answer:  16

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Explanation:

Equate s(t(x)) and s(1) to find that t(x) = 1 must be the case.

Let's find what x must be.

t(x) = 3x-8

1 = 3x-8

1+8 = 3x

9 = 3x

3x = 9

x = 9/3

x = 3

So plugging x = 3 into t(x) gets us t(x) = 1

In other words, t(3) = 1

So that tells us s(t(3)) = s(1)

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Let's plug x = 3 into the s(t(x)) equation

s(t(x)) = x^2 + 3x - 2

s(t(3)) = (3)^2 + 3(3) - 2

s(1) = 9 + 3(3) - 2

s(1) = 9 + 9 - 2

s(1) = 18 - 2

s(1) = 16