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if f(x)=2x+1 and g(x)=x^2-1, find (f/g)(x)

A. x^2 - 7 / 2x + 1
B. 2x + 1 / x^2 - 7
C. 2x + 1 / x^2 - 7, x ≠ ± square root 7
D. x^2 - 7 / 2x + 1, x ≠ - 1/2

Respuesta :

Given : f(x)=2x+1 and g(x)=x^2-1.

We need to find  (f/g)(x).

Note: In the given options, we have 2x + 1 and  x^2 - 7 parts.

So, let us take f(x)=2x+1 and g(x)=x^2-7.

[tex](f/g)(x) =\frac{f(x)}{g(x)}[/tex]

Plugging f and g functions in the formula.

[tex](\frac{f}{g})(x)=\frac{(2x+1)}{(x^2-7)}[/tex]

Also, it would be undefined for x = ± square root 7 becaue it would give 0 in the denomiantor.

Therefore, correct option is C. 2x + 1 / x^2 - 7, x ≠ ± square root 7.

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