$$Statement-1$$: f : R → R is a function defined by $$f(x)$$ $$=$$ $$5x$$ $$+$$ $$3$$. If g $$=$$ $$f-1$$, then $$g(x)$$ $$=$$ x $$-$$ $$3$$ $$5$$. $$Statement-2$$: If f : A→ B is a bijection and g : B → A is the inverse of f, then fog is the identity function on A.

Question

$$Statement-1$$: f : R → R is a function defined by $$f(x)$$ $$=$$ $$5x$$ $$+$$ $$3$$. If g $$=$$ $$f-1$$, then $$g(x)$$ $$=$$ x $$-$$ $$3$$ $$5$$. $$Statement-2$$: If f : A→ B is a bijection and g : B → A is the inverse of f, then fog is the identity function on A.

Infinity Learn · Accepted Answer

Let $$y=5x+3$$⇒$$x=y$$−$$35$$→ $$g(x)$$ $$=$$ x $$-$$ $$35$$ is the inverse of f, so $$statement-1$$ is $$TrueStatement-2$$ is false because g : B → A and f : A → B ⇒ fog : B→ B and g $$=$$ $$f-1$$ ⇒fog is an identity function on B.

Statement-1: f : $R \to R$ is a function defined by f(x) = 5x + 3. If $g = f^{- 1},$ then $g (x) = \frac{x - 3}{5} .$
Statement-2: If $f : A \to B$ is a bijection and $g : B \to A$ is the inverse of $f,$ then $f o g$ is the identity function on A.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Statement-1: f : R → R is a function defined by f(x) = 5x + 3. If g = f-1, then g(x) = x - 3 5. Statement-2: If f : A→ B is a bijection and g : B → A is the inverse of f, then fog is the identity function on A.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Statement-1: f : $R \to R$ is a function defined by f(x) = 5x + 3. If $g = f^{- 1},$ then $g (x) = \frac{x - 3}{5} .$
Statement-2: If $f : A \to B$ is a bijection and $g : B \to A$ is the inverse of $f,$ then $f o g$ is the identity function on A.