Question

1. $f(x)=4x + 1$; $f(c + 7)$
2. $h(x)=-9 - x$; $h(2k - 5)$

for questions 11 - 16, use the functions to the left.

1. $f(4)+9$
2. $-2cdot g(-5)$
3. $g(4)+g(-1)$
4. $3cdot h(2)-f(-9)$
5. if $f(x)=-13$, find $x$.
6. if $h(x)=39$, find $x$.
7. anthropologists use the length of certain bones of the human skeleton to estimate the height of the living person. one of these bones is the femur. to estimate the height in centimeters of a female with a femur length of $x$, the function $h(x)=61.41 + 2.32x$ can be used. find $h(46)$ and explain its meaning.

given the graph of $f(x)$, find each function value.
18.
19.

Explanation:

Step1: Solve for \(f(c + 7)\) in \(f(x)=4x + 1\)

Substitute \(x=c + 7\) into \(f(x)\): \(f(c + 7)=4(c + 7)+1=4c+28 + 1=4c+29\)

Step2: Solve for \(h(2k - 5)\) in \(h(x)=-9 - x\)

Substitute \(x = 2k-5\) into \(h(x)\): \(h(2k - 5)=-9-(2k - 5)=-9-2k + 5=-2k-4\)

Step3: Solve for \(f(4)+9\) in \(f(x)=4x + 1\)

First find \(f(4)\): \(f(4)=4\times4 + 1=16 + 1=17\). Then \(f(4)+9=17 + 9=26\)

Step4: Since \(g(x)\) is not given for \( - 2\cdot g(-5)\), we skip this for now.

Step5: Since \(g(x)\) is not given for \(g(4)+g(-1)\), we skip this for now.

Step6: Solve for \(3\cdot h(2)-f(-9)\) in \(h(x)=-9 - x\) and \(f(x)=4x + 1\)

Find \(h(2)\): \(h(2)=-9-2=-11\). Then \(3h(2)=3\times(-11)=-33\)
Find \(f(-9)\): \(f(-9)=4\times(-9)+1=-36 + 1=-35\)
So \(3h(2)-f(-9)=-33-(-35)=-33 + 35 = 2\)

Step7: Solve for \(x\) when \(f(x)=-13\) in \(f(x)=4x + 1\)

Set \(4x+1=-13\). Subtract 1 from both sides: \(4x=-13 - 1=-14\). Then divide by 4: \(x=-\frac{14}{4}=-\frac{7}{2}\)

Step8: Solve for \(x\) when \(h(x)=39\) in \(h(x)=-9 - x\)

Set \(-9 - x=39\). Add 9 to both sides: \(-x=39 + 9 = 48\). Multiply by - 1: \(x=-48\)

Step9: Solve for \(h(46)\) in \(h(x)=61.41+2.32x\)

Substitute \(x = 46\) into \(h(x)\): \(h(46)=61.41+2.32\times46=61.41+106.72=168.13\)
The meaning of \(h(46) = 168.13\) is that the estimated height in centimeters of a female with a femur length of 46 cm is 168.13 cm.

Answer:

1. \(4c + 29\)
2. \(-2k-4\)
3. \(26\)
4. Not solvable ( \(g(x)\) not given)
5. Not solvable ( \(g(x)\) not given)
6. \(2\)
7. \(-\frac{7}{2}\)
8. \(-48\)
9. \(h(46)=168.13\), it means the estimated height in cm of a female with a femur - length of 46 cm is 168.13 cm.