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marta [7]
3 years ago
9

F(-5) = -4, and f(5)= 2 linear equation satisfying the conditions , if possible

Mathematics
1 answer:
san4es73 [151]3 years ago
4 0

Given:

f(-5) = -4, and f(5)= 2.

To find:

The linear equation satisfying the conditions.

Solution:

We have,

f(-5) = -4, and f(5)= 2

It means the function passes through the points (-5,-4) and (5,2). So, the linear equation of the function f is

y-y_1=\dfrac{y_2-y_1}{x_2-x_2}(x-x_1)

y-(-4)=\dfrac{2-(-4)}{5-(-5)}(x-(-5))

y+4=\dfrac{2+4}{5+5}(x+5)

y+4=\dfrac{6}{10}(x+5)

On further simplification, we get

y+4=\dfrac{3}{5}(x+5)

y+4=\dfrac{3}{5}x+3

y=\dfrac{3}{5}x+3-4

y=\dfrac{3}{5}x-1

Putting y=f(x), we get

f(x)=\dfrac{3}{5}x-1

Therefore, the required function is f(x)=\dfrac{3}{5}x-1.

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