Check if the following function have an inverse function. If yes, fin

1.	Check if the following function have an inverse function. If yes, find the inverse function.f(x) = \(\frac{6x-7}3\)
Answer» f(x) = \(\frac{6x-7}3\) Let f(x₁ ) = f(x₂) \(\therefore\) \(\frac{6x_1-7}3=\frac{6x_2-7}3\) \(\therefore\) x₁ = x₂ ∴ f is a one-one function. f(x) = \(\frac{6x-7}3\) = y (say) \(\therefore\) For every y, we can get x \(\therefore\) f is an onto function. \(\therefore\) x = \(\frac{3y+7}6\) = f^-1(y) Replacing y by x, we get f^-1(x) = \(\frac{3x+7}6\)

Check if the following function have an inverse function. If yes, find the inverse function.f(x) = \(\frac{6x-7}3\)

Answer»

f(x) = \(\frac{6x-7}3\)

Let f(x₁ ) = f(x₂)

\(\therefore\) \(\frac{6x_1-7}3=\frac{6x_2-7}3\)

\(\therefore\) x₁ = x₂

∴ f is a one-one function.

f(x) = \(\frac{6x-7}3\) = y (say)

\(\therefore\) For every y, we can get x

\(\therefore\) f is an onto function.

\(\therefore\) x = \(\frac{3y+7}6\) = f^-1(y)

Replacing y by x, we get

f^-1(x) = \(\frac{3x+7}6\)