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Find [tex]\( f(1) \)[/tex] in this piecewise function:

[tex]\[ f(x) = \begin{cases}
-2x + 10 & \text{if } x \ \textless \ 2 \\
\frac{3}{2}x + 3 & \text{if } x \geq 2
\end{cases} \][/tex]

[tex]\[ f(1) = \, ? \][/tex]

Sagot :

GinnyAnswer
To find [tex]\( f(1) \)[/tex] for the given piecewise function, we need to determine which part of the piecewise function to use based on the value of [tex]\( x = 1 \)[/tex].

The piecewise function is defined as:
[tex]\[ f(x) = \begin{cases} -2x + 10 & \text{if } x < 2 \\ \frac{3}{2}x + 3 & \text{if } x \geq 2 \end{cases} \][/tex]

1. Identify the appropriate piece of the function:

Since [tex]\( x = 1 \)[/tex], and [tex]\( 1 < 2 \)[/tex], we will use the first part of the piecewise function: [tex]\( y = -2x + 10 \)[/tex].

2. Substitute [tex]\( x = 1 \)[/tex] into the function:

[tex]\[ y = -2(1) + 10 \][/tex]

3. Perform the arithmetic operations:

[tex]\[ y = -2 + 10 \][/tex]

[tex]\[ y = 8 \][/tex]

Thus, [tex]\( f(1) = 8 \)[/tex].
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