Question

1. evaluate $f(1)$

$f(y)=\sqrt4{5y + 76}$

1. evaluate $h(4)$

$h(a)=\sqrt3{7a - 12}$

1. evaluate $f(-4)$

$f(x)=\sqrt3{8x + 288}$

1. evaluate $h(-2)$

$h(n)=\sqrt{6n + 16}$

1. evaluate $f(-4)$

$f(x)=\sqrt{5x + 56}$

1. evaluate $f(-3)$

$f(c)=\sqrt{7c + 85}$

1. evaluate $h(4)$

$h(c)=\sqrt{6c + 12}$

1. evaluate $f(5)$

$f(m)=\sqrt3{5m - 150}$

1. evaluate $g(6)$

$g(k)=\sqrt3{6k - 161}$

1. evaluate $h(5)$

$h(x)=\sqrt3{4x - 363}$

Explanation:

Problem 1: Evaluate \( f(1) \) where \( f(g) = \sqrt[4]{5g + 76} \)

Step 1: Substitute \( g = 1 \) into the function

Substitute \( g = 1 \) into \( f(g) = \sqrt[4]{5g + 76} \), we get \( f(1) = \sqrt[4]{5(1) + 76} \)

Step 2: Simplify the expression inside the fourth - root

Calculate \( 5(1)+76=5 + 76=81 \)

Step 3: Evaluate the fourth - root

Since \( 3^4=81 \), then \( \sqrt[4]{81}=3 \)

Step 1: Substitute \( a = 4 \) into the function

Substitute \( a = 4 \) into \( h(a)=\sqrt[3]{7a - 12} \), we get \( h(4)=\sqrt[3]{7(4)-12} \)

Step 2: Simplify the expression inside the cube - root

Calculate \( 7(4)-12 = 28-12 = 16 \)

Step 3: Evaluate the cube - root

\( \sqrt[3]{16}=2\sqrt[3]{2} \) (or we can write it as \( \sqrt[3]{16} \) in simplest radical form)

Step 1: Substitute \( x=-4 \) into the function

Substitute \( x = - 4 \) into \( f(x)=\sqrt[3]{8x + 288} \), we get \( f(-4)=\sqrt[3]{8(-4)+288} \)

Step 2: Simplify the expression inside the cube - root

Calculate \( 8(-4)+288=-32 + 288 = 256 \)

Step 3: Evaluate the cube - root

\( \sqrt[3]{256}=4\sqrt[3]{4} \) (since \( 4^3\times4=64\times4 = 256 \))

Answer:

\( 3 \)

Problem 2: Evaluate \( h(4) \) where \( h(a)=\sqrt[3]{7a - 12} \)