A piecewise function 𝑓(𝑥) is defined as shown. 𝑓(𝑥)={ 3𝑥+5, 0≤𝑥<3−2𝑥+1, 3≤𝑥<7 𝑥+8, 7≤𝑥≤10Evaluate 𝑓(3) and 𝑓(7).Enter your answers in the boxes.𝑓(3)=
Question
A piecewise function 𝑓(𝑥) is defined as shown. 𝑓(𝑥)={ 3𝑥+5, 0≤𝑥<3−2𝑥+1, 3≤𝑥<7 𝑥+8, 7≤𝑥≤10Evaluate 𝑓(3) and 𝑓(7).Enter your answers in the boxes.𝑓(3)=
Solution
To evaluate the function 𝑓(𝑥) at 𝑥=3 and 𝑥=7, we need to determine which piece of the piecewise function to use for each value of 𝑥.
For 𝑓(3), we look at the intervals for 𝑥 and see that 3 falls in the second interval (3≤𝑥<7). So, we use the function -2𝑥+1. Substituting 𝑥=3 into this function gives us -2*3+1 = -6+1 = -5. So, 𝑓(3) = -5.
For 𝑓(7), we see that 7 falls in the third interval (7≤𝑥≤10). So, we use the function 𝑥+8. Substituting 𝑥=7 into this function gives us 7+8 = 15. So, 𝑓(7) = 15.
So, 𝑓(3) = -5 and 𝑓(7) = 15.
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