Question

.Find all points (x, y) where the functions f(x), g(x), h(x) have the same value:
f(x) = 2^x−5 + 3, g(x) = 2x − 5, h(x) = 8/x+ 10

Answer 1

Find all points (x, y) where the functions $f(x), g(x), h(x)$ have the same value:

$$f(x)=-2(x+5)+3, g(x)=2x-5, h(x)=\dfrac{8}{x}+10$$

$$f(x)=g(x)=>-2(x+5)+3=2x-5$$

$$-2x-10+3=2x-5$$

$$4x=-2$$

$$x=-0.5$$

$$g(-0.5)=2(-0.5)-5=-6=f(-0.5)$$

Check

$$h(-0.5)=\dfrac{8}{-0.5}+10=-6=f(-0.5)=g(-0.5)$$

Point $(-0.5, -6).$