The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
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g(x) = x/2
y=x
Simply stated, the inverse of a function is a function where the variables are reversed. If you have a function f(x) = y, the inverse is denoted as f-1(y) = x. Examples: y=x+3 Inverse is x=y+3, or y=x-3 y=2x+5 Inverse is x=2y+5, or y=(x-5)/2
To find the inverse of the function ( f(x) = -13x^2 ), we first rewrite it in terms of ( y ): ( y = -13x^2 ). Next, we solve for ( x ) in terms of ( y ): ( x^2 = -\frac{y}{13} ) leads to ( x = \pm \sqrt{-\frac{y}{13}} ). However, since the original function is not one-to-one (it fails the horizontal line test), it does not have a proper inverse across all real numbers. We can restrict the domain to ( x \geq 0 ) or ( x \leq 0 ) to find a valid inverse in those ranges.
If the quadratic function is f(x) = ax^2 + bx + c then its inverse isf'(x) = [-b + +/- sqrt{b^2 - 4*(c - x)}]/(2a)
X squared is not an inverse function; it is a quadratic function.
The inverse of the function y = x is denoted as y = x. The inverse function essentially swaps the roles of x and y, so the inverse of y = x is x = y. In other words, the inverse function of y = x is the function x = y.
The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
Given a function that is one-to-one and onto (a bijection), an inverse relationship is a function that reverses the action of the first function.A simple example to illustrate:if f(x) = x + 2, then g(x) = x - 2 is its inverse. fg(x) = x = gf(x).To find an inverse relationship of a function f(x)write y = f(x) as a function of xswap x and ymake the [new] y the subject of the formulathat is the inverse function.Going back to f(x) = x + 2write y = x + 2swap: x = y + 2make y the subject of the above equation: y = x - 2and so f'(x) is x - 2 where f'(x) represent the inverse of f(x).
To calculate the inverse of a square root function, you can start by expressing the square root function as ( y = \sqrt{x} ). To find the inverse, you swap ( x ) and ( y ), resulting in ( x = \sqrt{y} ). Then, solve for ( y ) by squaring both sides, giving you ( y = x^2 ). Thus, the inverse of the square root function is the square function, ( f^{-1}(x) = x^2 ).