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Stolb23 [73]
3 years ago
10

Lf f(x) = 5x, what is f^-1(x)?

Mathematics
1 answer:
Nonamiya [84]3 years ago
7 0

Answer: f^{-1}(x)=\frac{x}{5}

Step-by-step explanation:

By definition the domain of an inverse function f^-1(x) is the range of f(x) and the range of the inverse function is equal to the domain of the principal function f(x).

If you have a function f(x)=5x, then to find the inverse function, follow these steps:

1. Make y=f(x)

 f(x)=y=5x

 y=5x

2. Solve for the variable "x":

x=\frac{y}{5}

3. Exchange the variable "x" with the variable "y":

y=\frac{x}{5}

4. Exchange "y" withf^{-1}(x). Then the inverse function is:

f^{-1}(x)=\frac{x}{5}

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Solve the following inequality using both the graphical and algebraic approach: 0.5 x + 3 greater-than-or-equal-to 2 x minus 1.5
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Answer:

d. x les-than-or-equal-to 3 Graph B

Graph B expressed as follows; The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)

Step-by-step explanation:

The given inequality is expressed as follows;

0.5·x + 3 ≥ 2·x - 1.5

Let y₁ = 0.5·x + 3, and y₂ = 2·x - 1.5, we get;

For x = -1, 0, 1, 2, 3, 4, 5, 6

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y₂ = -3.5, -1.5, 0.5, 2.5, 4.5, 6.5, 8.5, 10.5

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The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)

Please find attached the required inequality created with MS Excel

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