Mathematics: Find the x-intercept f(x)=3^(x-1)-2

Find the x-intercept f(x)=3^(x-1)-2 - id312304769, treway3982

orlando19882000

10.03.2022

Hello!

The answer is:

The function intercepts de x-axis at "x" equal to 1.631.

Why?

To find the x-intercept of the function, we need to make f(x) or "y" equal to 0, and then, isolate "x".

So, isolating we have:

$f(x)=3^{(x-1)} -2\\\\0=3^{(x-1)} -2\\\\3^{(x-1)}=2\\\\Log_{3}(3^{(x-1)})=Log_{3}(2)\\\\x-1=0.631\\\\x=0.631+1=1.631$

Hence, we have that the function intercepts de x-axis at "x" equal to 1.631.

Have a nice day!

Note: I have attached a picture for better understanding.

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madams1820

04.01.2022

y – 1/3 = 3/4 (x – 4)

Step-by-step explanation:

The equation of a line is given by y-y_1=m(x-x_1)

Where

m is the slope, and

(x_1,y_1) is the coordinates of the point given

It is giventhat the slope is 3/4, so m = 3/4. Also, the point is (4, 1/3) so this is (x_1,y_1)

Plugging it into the formula, we get:

$y-y_1=m(x-x_1)\\y-\frac{1}{3}=\frac{3}{4}(x-4)$

Hence, 2nd option is the right answer.

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