For what values of x does f(x)=g(x)

Question

Given f(x) = x² - 1 and g(x) = 3^x, for what values of x does f(x)=g(x)?

Answer 1

x^2-1 =3^x

grap it and find where the curve intersects the x axis

about x=-1.15

use a graphing calculator, such as Desmos

for x=0

-1 =1

x=1

1-1 =3, 0=3

x=2

3 = 9

x=3

8 =27

if there's a solution x<0

x=-1

1-1 =0= 1/3

x=-2

3= 1/9

solution is somewhere -2<x<-1

as that's where it switches from x^2 -1<3^2 to x^2 -1> 3^2

try x=-1.15

1.3225-1 = 1/3^1.15

about .3 = about .3

x^2-1 = 3^x

(-1.15)^2 -1 = 3^(-1.15)

.3 = .3 rounded off

more precise accurate answer is

x = -1.13468

(-1.13468)^2 -1 = 3^(-1.13468)

1.287498702 - 1 = 1/3^1.13468

.287498702 = .28749872

rounded off it's

about .3 = .3 as in the 1st less precise solution x=1.15