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Can someone help!!!?

Can someone help!!!?-example-1
User Kiran K G
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1 Answer

4 votes

Answer:

f^(-1)(x) = 1/5x

Explanation:


\large{f(x) = mx + b \longrightarrow f^( - 1) (x) = (x - b)/(m) }

Inverse Function is when we swap the x-term and y-term. Here is an explanation to the inverse of linear function above.


\large{f(x) = mx + b}

Here we define f(x) = y. It is better to use y instead of f(x)


\large{y = mx + b}

Swap x-term and y-term.


\large{x = my + b}

Arrange/Simplify in the y-isolated equation.


\large{x - b = my} \\ \large {(x - b)/( m) = y} \\ \large{ y = (x - b)/(m) }

Since the function is in inverse form. It's recommended to use f^(-1) to point out that the function is an inverse of the original function.


\large \boxed{ {f}^( - 1) (x) = (x - b)/(m) }

Hence, y = (x-b)/m is an inverse of y = mx+b. A one-to-one function can have an inverse form. Back to the question!

We are given the linear function:


\large{f(x) = 5x}

We will be using substitution method by substituting the original function in inverse form.

Since we know that the slope is 5 and doesn't have y-intercept which is b-value. Hence


\large{ {f}^( - 1) (x) = (x - 0)/(5) } \\ \large{ {f}^( - 1) (x) = (x )/(5) } \\ \large{ {f}^( - 1) (x) = (1)/(5) x}

Or we swap x-term and y-term.


\large{f(x) = 5x} \\ \large{y = 5x} \\ \large{x = 5y} \\ \large{ (x)/(5) = y} \\ \large{y = (x)/(5) = (1)/(5) x} \\ \large{ {f}^( - 1) (x) = (1)/(5) x}

User Lashleigh
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