SOLUTION: Two functions f and g are such that f(x) = 1 + 2x and g(f(x)) = x + 3. What is the value of g(5)?

Question 1037620: Two functions f and g are such that f(x) = 1 + 2x and g(f(x)) = x + 3. What is the value of g(5)?
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Two functions f and g are such that f(x) = 1 + 2x and g(f(x)) = x + 3. What is the value of g(5)?
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g(f(x)) = x+3
g(1+2x) = 2x+4 = (1+2x)+3
If 1+2x = 5, then g(5) = 5+3 = 8
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Cheers,
Stan H.
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Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Both functions are linear in x.

Expect g(x) to be a linear function in x, and g might be kx+p, so start it as .

Given is the composition .

The two composition functions must be equal.

Identify and equate the corresponding parts.

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Return to the more variablized function , and substitute the values found.

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