Question

Please solve this problem and tell me which option is correct.

Answer 1

the answer is the first option
hope it helps
plz mark brainliest

Answer 2

Answer:

The correct option is b.

Step-by-step explanation:

The given function is

$f(x)=3x-5$

If $x_1=x_2$, then $f(x_1)=f(x_2)$, then f is one one function.

$3x_1-5=3x_2-5$

$3x_1=3x_2$

$x_1=x_2$

Therefore f is one one function.

If f(y)=x, then the function is onto.

Step 1: Substitute f(x)=y.

$y=3x-5$

Step 2: Interchange x and y.

$x=3y-5$

Step 3: Isolate y.

$x+5=3y$

$\frac{x+5}{3}=y$

Now find f(y).

$f(\frac{x+5}{3})=3(\frac{x+5}{3})-5=x$

Therefore f is onto function.

Step 4: Substitute y=f⁻¹(x).

$f^{-1}(x)=\frac{x+5}{3}$

The inverse of f(x) is $f^{-1}(x)=\frac{x+5}{3}$.

Therefore correct option is b.