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vekshin1
3 years ago
12

Please help! functions operations. explain please

Mathematics
1 answer:
QveST [7]3 years ago
6 0

Answer:

f(x)

Domain: all real numbers

Range:y\ge -2

f^{-1}(x)

Domain: y\ge -2

Range:all real numbers

Step-by-step 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 \sqrt{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 f^{-1}(x).

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 \sqrt{x+2}=y

f^{-1}(x)=\pm \sqrt{x+2}

Domain: x\ge-2

Range:

Let

y=\pm \sqrt{x+2}

\implies y^2-2=x

x is defined for all y-values.

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