Question

can someone help me with this question that is attached?

Answer 1

The value of f(g(x)) in the form a + bxⁿ is 1 -5x⁻². Where a = 1, b = -5 and n = -2

Determining the value of a function

From the question, we are to determine the value of f(g(x)) in the form a + bxⁿ

From the given information,

$f(x) = \frac{x}{x+5}$

and

$g(x) = x^{2} -5$

Then,

$f(g(x)) = \frac{(x^{2} -5)}{(x^{2} -5) +5}$

∴ $f(g(x)) = \frac{x^{2} -5}{x^{2} }$

Simplifying

$f(g(x)) = \frac{x^{2} }{x^{2} } -\frac{5}{x^{2}}$

$f(g(x)) = 1 -\frac{5}{x^{2}}$

$f(g(x)) = 1 -5x^{-2}$

Hence, the value of f(g(x)) in the form a + bxⁿ is 1 -5x⁻². Where a = 1, b = -5 and n = -2.

Learn more on Determining the value of a function here: https://brainly.com/question/2142762

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