Mathematics: Given f(x)=sec x and g(x)=arcsin x, what is f(g( answer choices: a. sqrt 1-x^2 / 1-x^2 b. sqrt x^2+1 / x^2+1 c. sqrt 1-x^2 d. sqrt x^2+1

Given f(x)=sec x and g(x)=arcsin x, what is f(g( - id5035340, allytrujillo20oy0dib

sugar1014

18.01.2022

Option 1 is correct.

Step-by-step explanation:

Given two functions f(x)=sec x and g(x)=arcsin x

we have to find f(g(x)).

f(g(x))=sec(arcsinx)=sec A where A=arc(sinx)

As, A=arc(sinx)

⇒ $x=sin A=\frac{P}{H}$

⇒ P=x and H=1 gives $B=\sqrt{1-x^2}$

hence, $sec A=\frac{H}{B}=\frac{1}{\sqrt{1-x^2}}$

hence, $f(g(x))=\frac{1}{\sqrt{1-x^2}}$

Rationalizing, we get

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

Option 1 is correct.

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