FunctionHard
Question
If g {f(x)} =| sin x | and f{g(x)} = (sin √x)2, then
Options
A.f(x) = sin2 x, g(x) = √x
B.f(x) = sin x, g(x) = | x |
C.f(x) = x2 , g(x) = √x
D.f and g cannot be determined
Solution
Let f (x) = sin2 x and g (x) = √x
Now, fog(x) = f[g(x)] = f(√x) = sin2 √x
and gof(x) = g[f(x)] = g(sin2x)
= |sin x|
Again let f(x) = sin x, g(x) = |x|
fog (x) = f[g(x)] = f(|x|) = sin |x| ≠ (sin √x)2
When f(x) = xx, g(x) = sin √x
fog(x) = f[g(x)] = f(sin √x) = (sin √x)2
and (gof)(x) = g[f(x)] = g(x2) = sin √x2
= sin |x| ≠ |sin x|
Therefore, (a) is the answer.
Now, fog(x) = f[g(x)] = f(√x) = sin2 √x
and gof(x) = g[f(x)] = g(sin2x)
= |sin x|Again let f(x) = sin x, g(x) = |x|
fog (x) = f[g(x)] = f(|x|) = sin |x| ≠ (sin √x)2
When f(x) = xx, g(x) = sin √x
fog(x) = f[g(x)] = f(sin √x) = (sin √x)2
and (gof)(x) = g[f(x)] = g(x2) = sin √x2
= sin |x| ≠ |sin x|
Therefore, (a) is the answer.
Create a free account to view solution
View Solution FreeMore Function Questions
Function f : → [− 1, 1], f(x) = sin x is -...If f : R → R, f(x) = x2 + 2x − 3 and g : R → R, g(x) = 3x − 4 , then the value of fog (x) is-...If the function. g(x) =is differentiable, then value of k + m is -...The fundamental period of the function, f(x) = x + a - [x + b] + sin πx + cos 2πx + sin 3πx + cos 4π...Let $\alpha,\beta$ be the roots of the quadratic equation $12x^{2} - 20x + 3\lambda = 0,\lambda \in \mathbb{Z}$. If $\fr...