Solve[x^5 - 2 == 1, 
      x]

N[%7]

g[x_] := x^5 - 2
ParametricPlot[{{x, g[x]}, {g[x], x}}, {x, 0, 4}, 
        PlotStyle -> {{}, Hue[0]}, 
        AspectRatio -> Automatic];

ParametricPlot[{{x, g[x]}, {g[x], x}}, {x, -4, 4}, 
        PlotStyle -> {{}, Hue[0]}, 
        AspectRatio -> Automatic];

f[x_] := Sin[x] - 2 Cos[x]
Plot[{f[x], 1}, {x, -8, 8}]

Solve[y -  2 Sqrt[1 - y^2] == 1,  y]

ArcSin[1]

Solve[y +  2 Sqrt[1 - y^2] == 1,  y]

N[- ArcSin[-3/5] +  Pi]

N[Pi/2 +  2 Pi]

N[- ArcSin[-3/5] +  Pi -  2 Pi]

N[Pi/2 -  2 Pi]

Plot[{f[x], 1}, {x, -0.46, 2.6}, 
      AspectRatio -> Automatic]

ParametricPlot[{{x, f[x]}, {f[x], x}}, {x, -0.46, 2.6}, 
        PlotStyle -> {{}, Hue[0]}, 
        AspectRatio -> Automatic];