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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]  14 May 2019, 09:12
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Question Stats:

88% (00:40) correct 11% (02:12) wrong based on 18 sessions
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]  14 May 2019, 11:37
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Expert's post
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 = $$\frac{3}{2}$$

Cheers,
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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