Question

Find the value of w (u(2))

Answer 1

Answer:  17

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Explanation:

We'll start things off by computing the inner function u(2)

Plug x = 2 into the u(x) function

u(x) = -x-1

u(2) = -2-1

u(2) = -3

This tells us that w(u(2)) is the same as w(-3). I replaced u(2) with -3.

We'll plug x = -3 into the w(x) function

w(x) = 2x^2-1

w(-3) = 2(-3)^2 - 1

w(-3) = 2(9) - 1

w(-3) = 18-1

w(-3) = 17

Therefore, w(u(2)) = 17

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Here's a slightly different approach:

Let's find what w(u(x)) is in general

w(x) = 2x^2 - 1

w(u(x)) = 2(u(x))^2 - 1

w(u(x)) = 2(-x-1)^2 - 1

Then we can plug in x = 2

w(u(x)) = 2(-x-1)^2 - 1

w(u(2)) = 2(-2-1)^2 - 1

w(u(2)) = 2(-3)^2 - 1

w(u(2)) = 2(9) - 1

w(u(2)) = 18 - 1

w(u(2)) = 17