Let $R$ be the set of real numbers and the functions $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x) = x^{2} + 2x - 3$ and $g(x) = x + 1$. Then, the value of $x$ for which $f(g(x)) = g(f(x))$ is

  • A
    -$1$
  • B
    $0$
  • C
    $1$
  • D
    $2$

Explore More

Similar Questions

Let $f: R \rightarrow R$ be defined by $f(x)=3 x^2-5$ and $g: R \rightarrow R$ by $g(x)=\frac{x}{x^2+1}$,then $g \circ f$ is

For $x \in R, x \neq 0,$ let $f_0(x) = \frac{1}{1 - x}$ and $f_{n + 1}(x) = f_0(f_n(x)),$ $n = 0, 1, 2, ....$ Then the value of $f_{100}(3) + f_1\left( \frac{2}{3} \right) + f_2\left( \frac{3}{2} \right)$ is equal to

If $f: R \rightarrow R$ is defined by $f(x) = (3 - x^3)^{\frac{1}{3}}$,then $f \circ (f \circ f)(x) = $ . . . . . . .

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$, where $[x]$ is the greatest integer not exceeding $x$, then for every $x \in R, f(g(x))$ is equal to

Consider $f: N \rightarrow N$,$g: N \rightarrow N$,and $h: N \rightarrow R$ defined as $f(x) = 2x$,$g(y) = 3y + 4$,and $h(z) = \sin z$,$\forall x, y, z \in N$. Show that $h \circ (g \circ f) = (h \circ g) \circ f$.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo