Problem

The following function is defined by two equations. The equation in the first row gives the output for values of $x$ less than 1. The equation in the second row gives the ouput for values of $x$ which are greater or equal to 1 .
\[
h(x)=\left\{\begin{array}{ll}
5 x+4 & \text { if } x< 1 \\
4 x-2 & \text { if } x \geq 1
\end{array}\right.
\]

Find the indicated values:
a) $h(3)=$
b) $h(-1)=$
c) $h(1)=$

Answer

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Answer

Final Answer: a) $h(3) = \boxed{10}$ b) $h(-1) = \boxed{-1}$ c) $h(1) = \boxed{2}$

Steps

Step 1 :We are given a function $h(x)$ which is defined by two equations. The equation in the first row gives the output for values of $x$ less than 1. The equation in the second row gives the output for values of $x$ which are greater or equal to 1.

Step 2 :The function is defined as follows: \[h(x)=\left\{\begin{array}{ll} 5 x+4 & \text { if } x<1 \\ 4 x-2 & \text { if } x \geq 1 \end{array}\right.\]

Step 3 :We are asked to find the values of the function $h(x)$ at $x=3$, $x=-1$, and $x=1$. The function is defined differently for $x<1$ and $x\geq1$. So, we need to use the appropriate equation for each value of $x$.

Step 4 :For $x=3$, since $3\geq1$, we use the equation $4x-2$. Substituting $x=3$ into the equation, we get $h(3) = 4*3 - 2 = 10$.

Step 5 :For $x=-1$, since $-1<1$, we use the equation $5x+4$. Substituting $x=-1$ into the equation, we get $h(-1) = 5*(-1) + 4 = -1$.

Step 6 :For $x=1$, since $1\geq1$, we use the equation $4x-2$. Substituting $x=1$ into the equation, we get $h(1) = 4*1 - 2 = 2$.

Step 7 :Final Answer: a) $h(3) = \boxed{10}$ b) $h(-1) = \boxed{-1}$ c) $h(1) = \boxed{2}$

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