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KiRa [710]
2 years ago
10

Given the function h(x), determine the functions which correctly decompose h(x) into component functions f(x) and g(x) so that h

(x) = f(g(x)).
$\tex$ h(x) = \sqrt{7x+2} - 10
Mathematics
1 answer:
nataly862011 [7]2 years ago
7 0

\text{Hi there! :)}

\large\boxed{g(x) = 7x + 2\text{ , } f(x) = \sqrt{x}  - 10}

\text{h(x) = f(g(x)), so determine what g(x) was substituted into f(x):}\\\\\text{Given the equation } h(x) = \sqrt{7x +2}- 10:\\\\\text{In the part of the equation with a variable, we see that "7x + 2" is in a square root:}

\text{Therefore, we can say that g(x) = 7x + 2:}\\\\\text{If h(x) = f(7x + 2), then f(x) must be:}\\\\f(x) = \sqrt{x} - 10

\text{The respective functions would be:}\\\\g(x) = 7x + 2\\\\f(x) = \sqrt{x}  - 10

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