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The functions f and g are defined as f(x) = 2x – 3 and g(x)
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14 May 2019, 09:12
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
(A) 1
(B) \(\frac{3}{2}\)
(C) 2
(D) 3
(E) 5
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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x)
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14 May 2019, 11:37
14 May 2019, 11:37
1
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
(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
Cheers,
Brent
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Re: The functions f and g are defined as f(x) = 2x – 3 and g(x)
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11 Dec 2021, 08:53
11 Dec 2021, 08:53
1
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 = \(\frac{3}{2}\)
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
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 = \(\frac{3}{2}\)
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
