Question

The graph below represents functions ƒ(x) and g(x).

Which value(s) of x makes ƒ(x) = g(x) a true statement?

0
1
2
3

Answer 1

1

Step-by-step explanation:

g(x) = 3^x + 1 and f(x) = 3x +1

For 0;

g(0) = 3^0 + 1 and f(0) = 3(0) + 1

g(0) = 1 + 1 f(0) = 1

g(0) = 2

Which is false.

For 1;

g(1) = 3^1 + 1 and f(1) = 3(1) + 1

g(1) = 3 + 1 f(1) = 3 + 1

g(1) = 4 f(1) = 4

Which is true.

For 2;

g(2) = 3^2 + 1 and f(2) = 3(2) + 1

g(2) = 9 + 1 f(2) = 6 + 1

g(2) = 10 f(2) = 7

Which is false.

For 3;

g(3) = 3^3 + 1 and f(2) = 3(3) + 1

g(3) = 27 + 1 f(2) = 9 + 1

g(3) = 28 f(2) = 10

Which is false.

Therefore, only 1 is the true answer.

Answer 2

For this case we have the following functions:
g (x) = 3 ^ x + 1
f (x) = 3x + 1
We observe that the graph of both functions are cut in the value of:
x = 1
Therefore, the value of the functions is the same for that value of x.
Let's check it: g (1) = 3 ^ 1 + 1 = 3 + 1 = 4
f (1) = 3 (1) + 1 = 3 + 1 = 4
Answer:
ƒ (x) = g (x) is a true statement for:
x = 1