Question

Cho hàm số y = f(x) = (m-1)x

a) Tìm m biết f(2) - f(-1) = 7

b) Cho m = 5. Tìm x biết f(3-2x) = 20

Answer 1

a, Ta có:

\(f\left(2\right)=\left(m-1\right).2=2m-2\)

\(f\left(-1\right)=\left(m-1\right).\left(-1\right)=-m+1\)

Theo bài ra ta có:
\(f\left(2\right)-f\left(-1\right)=7\)

\(\Rightarrow2m-2-\left(-m+1\right)=7\)

\(\Rightarrow2m-2+m-1=7\)

\(\Rightarrow3m=10\Rightarrow m=\dfrac{10}{3}\)

b, Ta có:

\(f\left(3-2x\right)=\left(5-1\right)\left(3-2x\right)=20\)

\(\Rightarrow4\left(3-2x\right)=20\)

\(\Rightarrow3-2x=5\Rightarrow2x=2\Rightarrow x=1\)

Chúc bạn học tốt!!!

Answer 2

a) \(f\left(2\right)-f\left(-1\right)=7\)

\(\Rightarrow\left(m-1\right)2-\left(m-1\right)\left(-1\right)=7\)

\(\Rightarrow2m-2+m-1=7\)

\(\Rightarrow3m=10\Rightarrow m=\dfrac{10}{3}\)

b) \(f\left(3-2x\right)=20\)

\(\Rightarrow\left(m-1\right)\left(3-2x\right)=20\)

\(\Rightarrow\left(5-1\right)\left(3-2x\right)=20\)

\(\Rightarrow4\left(3-2x\right)=20\)

\(\Rightarrow12-8x=20\)

\(\Rightarrow8x=12-20=-8\)

\(\Rightarrow x=-1\)

Answer 3

a) Ta có: f(2)-f(-1)=(m-1).2-[(m-1).(-1)]=7

<=> 2m-2+m-1=7 <=> 3m=10 => m=10/3

b) m=5 => f(x)=4x

 => f(3-2x)=4(3-2x)=20 <=> 3-2x=5 => 2x=-2 => x=-1