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otez555 [7]
3 years ago
8

Given that f(x)=x^2-4x -3 and g(x)=x+3/4 solve for f(g(x)) when x=9

Mathematics
1 answer:
SSSSS [86.1K]3 years ago
7 0

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

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Solve for x.<br> -4 &lt; 11 - 3.2
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Answer:

-4<11-(32/10)  

Inequality is always true

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.2" was replaced by "(32/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    -4-(11-(32/10))<0  

Step by step solution :

Step  1  :

           16

Simplify   ——

           5  

Equation at the end of step  1  :

              16

 -4 -  (11 -  ——)  < 0  

              5  

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

          11     11 • 5

    11 =  ——  =  ——————

          1        5    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

11 • 5 - (16)     39

—————————————  =  ——

      5           5  

Equation at the end of step  2  :

       39

 -4 -  ——  < 0  

       5  

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

          -4     -4 • 5

    -4 =  ——  =  ——————

          1        5    

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

-4 • 5 - (39)     -59

—————————————  =  ———

      5            5  

Equation at the end of step  3  :

 -59

 ———  < 0  

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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