If f(x)=(2 x-1/x+5), x ≠-5, then f-1(x) is equal to

Question

If f(x)=(2 x-1/x+5), x ≠-5, then f-1(x) is equal to (A) (x+5/2 x-1), x ≠ (1/2) (B) (5 x+1/2-x), x ≠ 2 (C) (x-3/2 x+1), x ≠ (1/2) (D) (5 x-1/2-x), x ≠ 2

Tardigrade Admin · Accepted Answer

Let y=(2 x-1/x+5) ⇒ x=(5 y+1/2-y) ∴ f-1(x)=(5 x-1/2-x), x ≠ 2

Q. If $f (x) = \frac{2 x - 1}{x + 5}, x \neq = - 5$ , then $f^{- 1} (x)$ is equal to

$\frac{x + 5}{2 x - 1}, x \neq = \frac{1}{2}$

$\frac{5 x + 1}{2 - x}, x \neq = 2$

$\frac{x - 3}{2 x + 1}, x \neq = \frac{1}{2}$

$\frac{5 x - 1}{2 - x}, x \neq = 2$

Let $y = \frac{2 x - 1}{x + 5}$
$\Rightarrow x = \frac{5 y + 1}{2 - y}$
$∴ f^{- 1} (x) = \frac{5 x - 1}{2 - x}, x \neq = 2$

Q. If f(x)=x+52x−1​,x=−5, then f−1(x) is equal to

2x−1x+5​,x=21​

2−x5x+1​,x=2

2x+1x−3​,x=21​

2−x5x−1​,x=2