Questions: If f(x)=int(3 x), find: (a) f(1.3) (b) f(3.2) (c) f(-1.7) (a) f(1.3)= (Simplify your answer.)

Transcript text: If $f(x)=\operatorname{int}(3 x)$, find: (a) $f(1.3)$ (b) $f(3.2)$ (c) $f(-1.7)$ (a) $f(1.3)=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Multiply the input $x$ by the coefficient $k$

To find the value of $f(x) = \operatorname{int}(kx)$ for $k = 3$ and $x = 1.3$, we first calculate the product $kx$. \[kx = 3 \times 1.3 = 3.9\]

Step 2: Apply the integer part function

Next, we apply the integer part function $\operatorname{int}(\cdot)$ to $kx$, which involves taking the integer part of $kx$, effectively discarding any fractional part. For $kx = 3.9$, the integer part is $\operatorname{int}(3.9) = 3$.

Final Answer:

The value of $f(x) = \operatorname{int}(kx)$ for $k = 3$ and $x = 1.3$ is $f(x) = 3$.

Step 1: Multiply the input $x$ by the coefficient $k$

To find the value of $f(x) = \operatorname{int}(kx)$ for $k = 3$ and $x = 3.2$, we first calculate the product $kx$. \[kx = 3 \times 3.2 = 9.6\]

Step 2: Apply the integer part function

Next, we apply the integer part function $\operatorname{int}(\cdot)$ to $kx$, which involves taking the integer part of $kx$, effectively discarding any fractional part. For $kx = 9.6$, the integer part is $\operatorname{int}(9.6) = 9$.

Final Answer:

The value of $f(x) = \operatorname{int}(kx)$ for $k = 3$ and $x = 3.2$ is $f(x) = 9$.

Step 1: Multiply the input $x$ by the coefficient $k$

To find the value of $f(x) = \operatorname{int}(kx)$ for $k = 3$ and $x = -1.7$, we first calculate the product $kx$. \[kx = 3 \times -1.7 = -5.1\]

Step 2: Apply the integer part function

Next, we apply the integer part function $\operatorname{int}(\cdot)$ to $kx$, which involves taking the integer part of $kx$, effectively discarding any fractional part. For $kx = -5.1$, the integer part is $\operatorname{int}(-5.1) = -5$.

Final Answer:

The value of $f(x) = \operatorname{int}(kx)$ for $k = 3$ and $x = -1.7$ is $f(x) = -5$.

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