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Find the indicated function values for the function [tex]g(x) = 8x + 8[/tex].

a. [tex]g(0)[/tex]

b. [tex]g(2)[/tex]

c. [tex]g\left(\frac{7}{8}\right)[/tex]

d. [tex]g(9b)[/tex]

e. [tex]g(b+4)[/tex]

a. [tex]g(0) = \square[/tex] (Simplify your answer.)


Sagot :

Sure, let's solve for the indicated function values for the function [tex]\( g(x) = 8x + 8 \)[/tex].

a. Finding [tex]\( g(0) \)[/tex]:
To find [tex]\( g(0) \)[/tex], we substitute [tex]\( x = 0 \)[/tex] into the function:

[tex]\[ g(0) = 8(0) + 8 = 8 \][/tex]

So, [tex]\( g(0) = 8 \)[/tex].

b. Finding [tex]\( g(2) \)[/tex]:
To find [tex]\( g(2) \)[/tex], we substitute [tex]\( x = 2 \)[/tex] into the function:

[tex]\[ g(2) = 8(2) + 8 = 16 + 8 = 24 \][/tex]

So, [tex]\( g(2) = 24 \)[/tex].

c. Finding [tex]\( g\left( \frac{7}{8} \right) \)[/tex]:
To find [tex]\( g\left( \frac{7}{8} \right) \)[/tex], we substitute [tex]\( x = \frac{7}{8} \)[/tex] into the function:

[tex]\[ g\left( \frac{7}{8} \right) = 8 \left( \frac{7}{8} \right) + 8 = 7 + 8 = 15 \][/tex]

So, [tex]\( g\left( \frac{7}{8} \right) = 15 \)[/tex].

d. Finding [tex]\( g(9b) \)[/tex]:
To find [tex]\( g(9b) \)[/tex], we substitute [tex]\( x = 9b \)[/tex] into the function:

[tex]\[ g(9b) = 8(9b) + 8 = 72b + 8 \][/tex]

Evaluating this expression further, let's simplify:

[tex]\[ g(9) = 72 + 8 = 80 \][/tex]

So, [tex]\( g(9b) = 80 \)[/tex].

e. Finding [tex]\( g(b+4) \)[/tex]:
To find [tex]\( g(b+4) \)[/tex], we substitute [tex]\( x = b+4 \)[/tex] into the function:

[tex]\[ g(b+4) = 8(b + 4) + 8 = 8b + 32 + 8 = 8b + 40 \][/tex]

Evaluating this expression further, let's simplify:

[tex]\[ g(4) = 32 + 8 = 40 \][/tex]

So, [tex]\( g(b+4) = 40 \)[/tex].

In summary:

a. [tex]\( g(0) = 8 \)[/tex]

b. [tex]\( g(2) = 24 \)[/tex]

c. [tex]\( g\left( \frac{7}{8} \right) = 15 \)[/tex]

d. [tex]\( g(9) = 80 \)[/tex]

e. [tex]\( g(4) = 40 \)[/tex]