Please help! functions operations. explain please

Question

asked Dec 25, 2020 34.8k views

1 Answer

Badal Shah · Answer 1 · 2020-12-29T16:15:38+0000

Answer:

f(x)

Domain: all real numbers

Range:
$y\ge -2$

f^(-1)(x)

Domain:
$y\ge -2$

Range:all real numbers

Explanation:

Given
f(x)=x^2-2

The domain of this function, refers to all values of x for which f(x) is defined.

The given function is a quadratic polynomial.

Polynomial functions are defined everywhere, therefore the domain is all real numbers.

The range refers to the values of y, for which x is defined

Let
y=x^2-2

Solve for x;

$x=\pm √(y+2)$

This function is defined for
$y+2\ge0$

This implies that;
$y\ge-2$

Inverse Function

The domain of f(x) becomes the range of
f^(-1)(x) and the range of f(x) becomes the domain of
.

Domain:
$y\ge -2$

Range:all real numbers

Or see it in details

Let
y=x^2-2

interchange x and y;

x=y^2-2

x+2=y^2

$\pm √(x+2)=y$

$f^(-1)(x)=\pm √(x+2)$

Domain:
$x\ge-2$

Range:

Let

$y=\pm √(x+2)$

$\implies y^2-2=x$

x is defined for all y-values.