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catdog2230
07.09.2020 •
Mathematics
Jim was given three functions and asked to determine ƒ + (g ○ h). The functions were ƒ (x) = x2, g(x) = 3x + 1, and h(x) = 2x. Jim started by writing the problem as (ƒ + (g ○ h))(x) = x2 + 2(3x + 1). What was Jim's mistake? What is the correct solution?
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Ответ:
[f + (g o h)](x) = x² + 6x + 1
Step-by-step explanation:
Given functions are,f(x) = x²
g(x) = 3x + 1
h(x) = 2x
Now we have to find the value of composite function [f + (g o h)](x).
(g o h)(x) = g[h(x)]
= 3(2x) + 1
= 6x + 1
[f + (g o h)](x) = f(x) + (g o h)(x)
= x² + 6x + 1
But Jim got the answer as,
[f + (g o h)](x) = x² + 2(3x + 1)
= x² + 6x + 2
Therefore, Jim's answer was incorrect.
Correct answer will be [f + (g o h)](x) = x² + 6x + 1
Ответ:
the 4th quadrant
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