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The functions f and g are defined as f(x) = 2x – 3 and g(x)

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The functions f and g are defined as f(x) = 2x – 3 and g(x) [#permalink] New post 14 May 2019, 09:12
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The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + \(\frac{3}{2}\). For what value of y is f(y) = g(y – 3) ?

(A) 1

(B) \(\frac{3}{2}\)

(C) 2

(D) 3

(E) 5
[Reveal] Spoiler: OA

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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x) [#permalink] New post 14 May 2019, 11:37
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Carcass wrote:
The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + \(\frac{3}{2}\). For what value of y is f(y) = g(y – 3) ?

(A) 1

(B) \(\frac{3}{2}\)

(C) 2

(D) 3

(E) 5


If f(x) = 2x – 3, then f(y) = 2y – 3

If g(x) = x + \(\frac{3}{2}\), then g(y – 3) = y – 3 + \(\frac{3}{2}\)


We want: f(y) = g(y – 3)

We can rewrite this equation as: 2y – 3 = y – 3 + \(\frac{3}{2}\)

Add 3 to both sides to get: 2y = y + \(\frac{3}{2}\)

Subtract y from both sides to get: y = \(\frac{3}{2}\)

Answer: B

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Brent
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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x)   [#permalink] 14 May 2019, 11:37
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