Math Problem Statement

Consider the function

If necessary, give answers as fractions in simplest for. For example: -3/2

Find the following.

(a) h(5) = Answer 1 Question 12 

(b) h(3) = Answer 2 Question 12 

(c) h(0) =Answer 3 Question 12 

(d) h(1/2) = Answer 4 Question 12 

Solution

You didn't specify the function, but I’ll assume it's the same function as before:

h(x)=2x+1x+5h(x) = \frac{2x + 1}{x + 5}

If this is correct, let's proceed to find the values for the given inputs.

(a) Finding h(5)h(5):

Substitute x=5x = 5 into the function:

h(5)=2(5)+15+5=10+110=1110h(5) = \frac{2(5) + 1}{5 + 5} = \frac{10 + 1}{10} = \frac{11}{10}

So, the answer to (a) is:

1110\boxed{\frac{11}{10}}

(b) Finding h(3)h(3):

Substitute x=3x = 3 into the function:

h(3)=2(3)+13+5=6+18=78h(3) = \frac{2(3) + 1}{3 + 5} = \frac{6 + 1}{8} = \frac{7}{8}

So, the answer to (b) is:

78\boxed{\frac{7}{8}}

(c) Finding h(0)h(0):

Substitute x=0x = 0 into the function:

h(0)=2(0)+10+5=15h(0) = \frac{2(0) + 1}{0 + 5} = \frac{1}{5}

So, the answer to (c) is:

15\boxed{\frac{1}{5}}

(d) Finding h(12)h\left(\frac{1}{2}\right):

Substitute x=12x = \frac{1}{2} into the function:

h(12)=2(12)+112+5=1+112+102=2112=2×211=411h\left(\frac{1}{2}\right) = \frac{2\left(\frac{1}{2}\right) + 1}{\frac{1}{2} + 5} = \frac{1 + 1}{\frac{1}{2} + \frac{10}{2}} = \frac{2}{\frac{11}{2}} = 2 \times \frac{2}{11} = \frac{4}{11}

So, the

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Math Problem Analysis

Mathematical Concepts

Functions
Rational Expressions
Substitution

Formulas

h(x) = (2x + 1) / (x + 5)

Theorems

Basic Function Evaluation

Suitable Grade Level

Grades 9-11