.The/function/f/satisfies/f(√x+1)=1x/for/all/x≥−1,x≠0.Findf(2).
2.Let/f(x)=3x2−4x.Find/the/constant/k/such/that/f(x)=f(k−x)for/all/real/numbers/x.
3.
4.
2. Let f(x) = 3x2 - 4x . Find the constant k such that f(x) = f(k - x) for all real numbers x .
f(x) = f(k - x)
And f(x) = 3x2 - 4x
3x2 - 4x = f(k - x)
And f(k - x) = 3(k - x)2 - 4(k - x)
3x2 - 4x = 3(k - x)2 - 4(k - x)
3x2 - 3(k - x)2 - 4x + 4(k - x) = 0
3[x2 - (k - x)2] - 4[x - (k - x)] = 0
3[x + (k - x)][x - (k - x)] - 4[x - (k - x)] = 0
3[x + k - x][x - k + x] - 4[x - k + x] = 0
3[ k ][ 2x - k ] - 4[ 2x - k ] = 0
( 2x - k )( 3k - 4 ) = 0
2x - k = 0 or 3k - 4 = 0
k = 2x k = 4/3
The constant value that works is k = 4/3