Question

Given f(x)=sec x and g(x)=arcsin x, what is f(g(x))?

Answer 1

Answer:

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.