A aalpha New member Joined May 16, 2012 Messages 1 May 16, 2012 #1 Can anyone help me to solve the following problem. Of course its not home work problem.. thank you in advance.. f(x) = x2 + 3 gf = 2x2 + 3 find function g. kindly explain me such type of problem..
Can anyone help me to solve the following problem. Of course its not home work problem.. thank you in advance.. f(x) = x2 + 3 gf = 2x2 + 3 find function g. kindly explain me such type of problem..
S soroban Elite Member Joined Jan 28, 2005 Messages 5,584 May 16, 2012 #2 Hello, aalpha! \(\displaystyle f(x) \:=\: x^2+ 3\) \(\displaystyle g(f(x))\:=\: 2x^2+ 3\) \(\displaystyle \text{Find function }g(x).\) Click to expand... I had to baby-talk my way through it . . . We want a function \(\displaystyle g(x)\) which will change \(\displaystyle x^2+3\) to \(\displaystyle 2x^2+3\) We have: .\(\displaystyle f(x) \:= \: x^2+3\) Subtract 3: .\(\displaystyle f(x) - 3 \:=\: x^2\) Multiply by 2: .\(\displaystyle 2[f(x)-3] \:=\:2x^2\) Add 3: .\(\displaystyle 2[f(x) - 3] + 3 \:=\:2x^2+3\) Hence, the \(\displaystyle g\)-function is: "subtract 3, multiply by 2, add 3". Therefore: .\(\displaystyle g(x) \;=\;2(x-3) + 3 \;=\;2x-3\)
Hello, aalpha! \(\displaystyle f(x) \:=\: x^2+ 3\) \(\displaystyle g(f(x))\:=\: 2x^2+ 3\) \(\displaystyle \text{Find function }g(x).\) Click to expand... I had to baby-talk my way through it . . . We want a function \(\displaystyle g(x)\) which will change \(\displaystyle x^2+3\) to \(\displaystyle 2x^2+3\) We have: .\(\displaystyle f(x) \:= \: x^2+3\) Subtract 3: .\(\displaystyle f(x) - 3 \:=\: x^2\) Multiply by 2: .\(\displaystyle 2[f(x)-3] \:=\:2x^2\) Add 3: .\(\displaystyle 2[f(x) - 3] + 3 \:=\:2x^2+3\) Hence, the \(\displaystyle g\)-function is: "subtract 3, multiply by 2, add 3". Therefore: .\(\displaystyle g(x) \;=\;2(x-3) + 3 \;=\;2x-3\)
