For the function f(x)=(7)/(2x+7), find f^(-1)(x). Answer: f^(-1)(x)=

Rewrite function with y: To find the inverse function, f^(-1)(x), we need to switch the roles of x and y in the original function and then solve for y. Let's start by rewriting the function with y instead of f(x): y = (7)/(2x + 7)Switch x and y: Now, switch x and y to find the inverse: x = (7)/(2y + 7)Multiply both sides: Next, we solve for y. Start by multiplying both sides of the equation by (2y + 7) to get rid of the fraction: x(2y + 7) = 7Distribute x: Distribute x on the left side of the equation: 2xy + 7x = 7Isolate term with y: Now, we want to isolate the term with y in it, so subtract 7x from both sides: 2xy = 7 - 7xDivide both sides: To solve for y, divide both sides by 2x: y = (7 - 7x) / (2x)Simplify the expression: Finally, we can simplify the expression by factoring out the 7 in the numerator: y = 7(1 - x) / (2x)Inverse function: This gives us the inverse function: f^(-1)(x) = 7(1 - x) / (2x)

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For the function
f(x)=(7)/(2x+7), find
f^(-1)(x).
Answer:
f^(-1)(x)=

For the function $f(x)=\frac{7}{2 x+7}$ , find $f^{-1}(x)$ . $\newline$ Answer: $f^{-1}(x)=$

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Algebra 2

Write a formula for an arithmetic sequence

Full solution

Q. For the function

f(x)=\frac{7}{2 x+7}

, find

f^{-1}(x)

\newline

Answer:

f^{-1}(x)=

Rewrite function with y: To find the inverse function, $f^{-1}(x)$ , we need to switch the roles of $x$ and $y$ in the original function and then solve for $y$ . Let's start by rewriting the function with $y$ instead of $f(x)$ : $\newline$ $y = \frac{7}{2x + 7}$
Switch x and y: Now, switch x and y to find the inverse: $x = \frac{7}{2y + 7}$
Multiply both sides: Next, we solve for $y$ . Start by multiplying both sides of the equation by $(2y + 7)$ to get rid of the fraction: $\newline$ $x(2y + 7) = 7$
Distribute $x$ : Distribute $x$ on the left side of the equation: $2xy + 7x = 7$
Isolate term with y: Now, we want to isolate the term with $y$ in it, so subtract $7x$ from both sides: $2xy = 7 - 7x$
Divide both sides: To solve for $y$ , divide both sides by $2x$ : $y = \frac{7 - 7x}{2x}$
Simplify the expression: Finally, we can simplify the expression by factoring out the $7$ in the numerator: $y = \frac{7(1 - x)}{2x}$
Inverse function: This gives us the inverse function: $f^{-1}(x) = \frac{7(1 - x)}{2x}$