4.3: 评估函数
计算函数时,将 x 替换为给定的数值或代数表达式,然后简化结果。
假定f(x)=−x2+5x+12,找到以下各项:
- f(2)
- f(−5)
- f(t)
- f(4x−1)
解决方案
- 替换x为2:
f(x)=−x2+5x+12Given equationf(2)=−(22)+5∗2+12Replace x with 2 - notice that only 2 is squared, not the minus signf(2)=−4+10+12Simplifyf(2)=18Solution
- 替换x为−5:
f(x)=−x2+5x+12Given equation f(−5)=−((−5)2)+5∗(−5)+12Replace x with −5 - notice that it’s −x2 , so the −5 is squared, but the result is still negativef(2)=−25+(−25)+12Simplify f(2)=−38Solution
- 替换x为t:
f(x)=−x2+5x+12Given equation f(t)=−t2+5∗(t)+12Replace x with t f(t)=−t2+5t+12Simplify
- 替换x为(4x−1):
f(x)=−x2+5x+12Given equationf(4x−1)=−(4x−1)2+5∗(4x−1)+12Replace x with (4x−1)f(4x−1)=−(16x2−8x+1)+20x−5+12Expand(4x−1)2 and distribute the 5 to (4x−1)f(4x−1)=−16x2+8x−1+20x−5+12Distribute the negative signf(4x−1)=16x2+28x+6Simplify
- 对于该函数f(x)=x3−9,请找到
- f(3)
- f(2x−5)
- f(t)
- 对于该函数f(x)=x2−4x+1,请找到
- f(2)
- f(4x+3)
- f(z)
- 对于该函数f(x)=x4+9x2−6x−1,请找到
- f(1)
- f(x+2)
- f(a)