The following function may be viewed as a composite function f(g(x)). Find f(x) and g(x). $\frac { 1 } { x ^ { 2 } + 2 x - 3 }$
A) f(x) = x, G(x) = $x ^ { 2 }$ + 2x - 3
B) f(x) = $\frac { 1 } { x }$, G(x) = $\frac { 1 } { x ^ { 2 } + 2 x - 3 }$
C) f(x) = $\frac { 1 } { x }$, G(x) = $x ^ { 2 }$ + 2x - 3
D) f(x) = $x ^ { 2 }$ + 2x - 3, G(x) = $\frac { 1 } { x }$

Question

Quizplus · Accepted Answer

The given function can be decomposed into $f(x) = \frac{1}{x}$ and $g(x) = x^2 + 2x - 3$, where $g(x)$ represents the quadratic expression inside the function and $f(x)$ represents the reciprocal of $x$.

The Following Function May Be Viewed as a Composite Function 1x2+2x−3\frac { 1 } { x ^ { 2 } + 2 x - 3 }x2+2x−31​

The Following Function May Be Viewed as a Composite Function $\frac { 1 } { x ^ { 2 } + 2 x - 3 }$