The exponential function g, represented in the table, can be written as g(x) = a. b.
2
O
1
g(2)
12
9
REFRESH
THE
Complete the equation for g(x).
g(x) =
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Explanation:

Since the function and the table are garbled, I will explain you how to deal with this kind of questions with the function g(x) = a.bˣ, and the table:

   x     g(x)

   0    12

   1      9

To complete the equation g(x) you must find a and b.

To find a, you can use the initial pair (0, 12), x = 0, g(0) = 12.

Thus, the function is g(x) = 12 . (b)ˣ

Use the second pair (1, 9):

Hence, the function g(x) is:

You might, for instance, find g(2):

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

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step-by-step explanation: