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# The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + 3/2.

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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + 3/2. [#permalink]
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Bunuel wrote:
The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + 3/2. For what value of y is f(y) = g(y – 3) ?

(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 5

APPROACH #1: Algebraic methods

GIVEN: f(x) = 2x – 3 and g(x) = x + 3/2

So, f(y) = 2y – 3
And g(y-3) = (y - 3) + 3/2 = y - 1.5

So, if f(y) = g(y – 3), we can write: 2y – 3 = y - 1.5
Add 3 to both sides: 2y = y + 1.5
Subtract y from both sides: y = 1.5 (aka 3/2)

--------------------------------------
APPROACH #2: Testing the answer choices

A) 1
If y = 1, does f(y) = g(y – 3)?
Let's check.

Replace y with 1 to get:
f(1) = 2(1) - 3 = -1
g(1 – 3) = g(-2) = -2 + 3/2 = 0.5
No good.

B) 3/2
Let's use 1.5 instead of 3/2
If y = 1.5, does f(y) = g(y – 3)?
Let's check.
Replace y with 1.5 to get:
f(1.5) = 2(1.5) - 3 = 0
g(1.5 – 3) = g(-1.5) = -1.5 + 3/2 = 0
PERFECT!

Cheers,
Brent
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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + 3/2. [#permalink]
Bunuel wrote:
The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + 3/2. For what value of y is f(y) = g(y – 3) ?

(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 5

Since f(y) = 2y - 3 and g(y - 3) = y - 3 + 3/2, so we have:

2y - 3 = y - 3 + 3/2

y = 3/2

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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x) = x + 3/2. [#permalink]
Top Contributor
Given that f(x) = 2x – 3 and g(x) = x + $$\frac{3}{2}$$ and we need to find the value of y for which f(y) = g(y – 3)

Let's find out the value of f(y) first
To find f(y) we need to put x=y in f(x)
=> f(y) = 2y - 3

Let's find g(y-3) now
To find g(y-3) we need to put x=y-3 in g(x)
=> g(y-3) = y-3 + $$\frac{3}{2}$$ = y - $$\frac{3}{2}$$

f(y) = g(y-3)
=> 2y - 3 = y - $$\frac{3}{2}$$
=> 2y - y = 3 - $$\frac{3}{2}$$
=> y = $$\frac{3}{2}$$