Question

If f : R → R, g : R → R and h : R → R is such that f(x) = x2, g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = π√2 will be​

Answer 1

EXPLANATION.

⇒ If f : R ⇒ R, g : R ⇒ R, h : R ⇒ R.

⇒ f(x) = x².

⇒ g(x) = tan(x).

⇒ h(x) = ㏒(x).

⇒ x = π/√2.

As we know that,

To find :

⇒ [ho(gof)].

⇒ [ho (g f(x))]

⇒ g f(x) = tan(x²).

⇒ [h (g f(x))] = ㏒(g f(x)).

⇒ [ho(gof)]. = ㏒(tanx²).

⇒ [ho(gof)].(π/√2) = ㏒[tan(π/√2)²].

⇒ [ho(gof)]. = ㏒[tan(π²/2)].

                                                                                                                         

MORE INFORMATION.

Interval.

(1) = Close interval [a, b] = {x, a ≤ x ≤ b}.

(2) = Open interval (a, b) or ]a, b[ = {x, a < x < b}.

(3) = Semi open or semi close interval.

[a, b[ or [a, b) = {x ; a ≤ x < b}.

]a, b] or (a, b] = {x ; a < x ≤ b}.

Answer 2

$\huge\mathcal{\pink{A}}\huge\mathcal{\purple{N}}\huge\mathcal{\green{S}}\huge\mathcal{\blue{W}}\huge\mathcal{\red{E}}\huge\mathcal{R}$

⇒ If f : R ⇒ R, g : R ⇒ R, h : R ⇒ R.

⇒ f(x) = x².

⇒ g(x) = tan(x).

⇒ h(x) = ㏒(x).

⇒ x = π/√2.

As we know that,

To find :

⇒ [ho(gof)].

⇒ [ho (g f(x))]

⇒ g f(x) = tan(x²).

⇒ [h (g f(x))] = ㏒(g f(x)).

⇒ [ho(gof)]. = ㏒(tanx²).

⇒ [ho(gof)].(π/√2) = ㏒[tan(π/√2)²].

⇒ [ho(gof)]. = ㏒[tan(π²/2)].

                                                                                                                         

_______________________________________________________________