Question

Find the rule of the function $f\circ g$. $\frac{1}{2x+7}$ and $g(x) = x^2 - 7$ $f(x) =$ $f(g(x)) = \frac{1}{(2x^2 - 7)^2} - 7$ $f(g(x)) = \frac{1}{7x^2}$ $f(g(x)) = \frac{1}{2x^2 - 7}$ $f(g(x)) = \frac{2}{7x^2 + 7}$ $f(g(x)) = \frac{1}{7x^2 - 49}$

          Find the rule of the function $f\circ g$.
$\frac{1}{2x+7}$ and $g(x) = x^2 - 7$
$f(x) =$
$f(g(x)) = \frac{1}{(2x^2 - 7)^2} - 7$
$f(g(x)) = \frac{1}{7x^2}$
$f(g(x)) = \frac{1}{2x^2 - 7}$
$f(g(x)) = \frac{2}{7x^2 + 7}$
$f(g(x)) = \frac{1}{7x^2 - 49}$

Find the rule of the function f∘ g.
(1)/(2x+7) and g(x) = x^2 - 7
f(x) =
f(g(x)) = (1)/((2x^2 - 7)^2) - 7
f(g(x)) = (1)/(7x^2)
f(g(x)) = (1)/(2x^2 - 7)
f(g(x)) = (2)/(7x^2 + 7)
f(g(x)) = (1)/(7x^2 - 49)

Added by Leah B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Joseph Liao

10/29/2020

Step 1

We need to find the rule of the function fog, which is the composition of functions f and g. Step 2: Analyze the given forms of f(g(x)) We can see that all the given forms of f(g(x)) are in the form of a fraction with a numerator of 1 and a denominator that is a Show more…

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f(g(x))=(1)/((2x^(2)-7)+7) f(g(x))=(1)/(2x^(2)) f(g(x))=(1)/(2x^(2)-7) f(g(x))=(2)/(7x^(2)+7) f(g(x))=(1)/(7x^(2)-49) Find the rule of the function fog 1 fgx= 2x^2-7 1 = (x^2) 1 Ofg(x)=2x^2-7 2 +=(x^2)