Question

Square Root Function and inverse

Answer 1

The square root function 'undoes' the square function. It is denoted by the symbol √ and is the inverse of the square. You can find the square root of a number using a calculator or by using exponentiation and logarithm functions as alternative methods.

Step-by-step explanation:

The square root function is a mathematical operation that 'undoes' its counterpart, the square. It is denoted by the symbol √. For example, the square root of 16 is 4, because 4² = 16. The square root is the inverse of the square function. To find the square root of a number, you can use a calculator, or you can use the exponentiation and logarithm functions as alternative methods.

For example, to find the square root of 25 using exponentiation, you can raise 25 to the power of 1/2, which is equal to √25. Similarly, you can use the natural logarithm function to find the square root. Taking the natural logarithm of a number, x, and then raising e to the power of (ln x)/2 will give you the square root of x.

Answer 2

`f^-^1(x)=(x+1)/(8)`

Step-by-step explanation:

f(x) = 8x - 1

==> replace "f(x)" with y

y = 8x - 1

==> inter exchange x and y

x = 8y - 1

==> solve for y now, first step would be to add 1 to both sides

x + 1 = 8y

==> divide both sides by 8

(x+1)/8 = y

==> replace y with f^-1(x)

f^-1(x)=(x+1)/8y